An Analysis of the Performance of the SPRT Chart with Estimated Parameters Under the Weibull Distribution

Most developments of the sequential probability ratio test (SPRT) control chart assume that the underlying process comes from a Normal distribution with known mean and standard deviation. Nevertheless, the true values of the process parameters are usually inaccessible in production settings, and they must be approximated from a set of Phase-I data. In certain areas, the process data can be positively skewed, which in turn affect the performance of control charts designed under the Normal distribution. In this paper, we provide a thorough analysis on the performances of the SPRT chart with estimated process parameters under the influence of Weibull distributed data. The unconditional properties of the expected value and standard deviation of the time to signal are evaluated using Monte Carlo simulation to facilitate comparisons between the Normal and Weibull distributions. Results show that both the in-control and out-of-control performances of the SPRT chart deteriorate when Weibull data are used. However, the optimal design of the SPRT chart with estimated process parameters seems to reverse the effect for large process mean shifts.